CLASSIFICATION OF TWO TYPES OF WEAK SOLUTIONS TO THE CASIMIR EQUATION FOR THE ITO SYSTEM
Abbreviated Journal Title
Q. Appl. Math.
Casimir equation; Ito system; extended KdV equation; weak solutions; asymptotic series; Mathematics, Applied
The existence and non-uniqueness of two classes of weak solutions to the Casimir equation for the Ito system is discussed. In particular, for (i) all possible travelling wave solutions and (ii) one vital class of self-similar solutions, all possible families of local power series solutions are found. We are then able to extend both types of solutions to the entire real line, obtaining separate classes of weak solutions to the Casimir equation. Such results constitute rare globally valid analytic solutions to a class of nonlinear wave equations. Closed-form asymptotic approximations are also given in each case, and these agree nicely with the numerical solutions available in the literature.
Quarterly of Applied Mathematics
"CLASSIFICATION OF TWO TYPES OF WEAK SOLUTIONS TO THE CASIMIR EQUATION FOR THE ITO SYSTEM" (2014). Faculty Bibliography 2010s. 5425.